“Drama” in this sense, which I don’t think the OP elaborated on enough, is basically “media coverage”. This article, by existing, makes Kaep less likely to sign with a team. That Seattle Alderman advocating for Kaep makes him less likely to sign. Anytime someone goes on ESPN/Fox and talks about him (good or bad) makes him less likely to sign. The inevitability of Bob Costas bringing it up before Sunday Night Football makes him less likely to sign.
Its no longer (primarily) about his protest, its about the media circus. If the people who want Kaep to find a starting/backup job stopped saying it so loudly, it would be more likely to happen.